Everett Clarence Dade is a

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

University of Illinois at Urbana–Champaign The University of Illinois Urbana-Champaign (UIUC, U of I, Illinois, or University of Illinois) is a public land-grant research university in the Champaign–Urbana metropolitan area, Illinois, United States. Established in 1867, it is the f ...

working on

finite group In abstract algebra, a finite group is a group whose underlying set is finite. Finite groups often arise when considering symmetry of mathematical or physical objects, when those objects admit just a finite number of structure-preserving tra ...

s and

representation theory Representation theory is a branch of mathematics that studies abstract algebra, abstract algebraic structures by ''representing'' their element (set theory), elements as linear transformations of vector spaces, and studies Module (mathematics), ...

, who introduced the

Dade isometry In mathematical finite group theory, the Dade isometry is an isometry from class function on a subgroup ''H'' with support on a subset ''K'' of ''H'' to class functions on a group ''G'' . It was introduced by as a generalization and simplification ...

and

Dade's conjecture In finite group theory, Dade's conjecture is a conjecture relating the numbers of characters of blocks of a finite group to the numbers of characters of blocks of local subgroup In group theory, a branch of mathematics, a subset of a group G is ...

. While an undergraduate at

Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...

, he became a

Putnam Fellow The William Lowell Putnam Mathematical Competition, often abbreviated to Putnam Competition, is an annual mathematics competition for undergraduate college students enrolled at institutions of higher learning in the United States and Canada (regar ...

twice, in 1955 and 1957.

Work

The

is an

isometry In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective. The word isometry is derived from the Ancient Greek: ἴσος ''isos'' me ...

from

class function In mathematics, especially in the fields of group theory and representation theory of groups, a class function is a function on a group ''G'' that is constant on the conjugacy classes of ''G''. In other words, it is invariant under the conjugati ...

s on a

subgroup In group theory, a branch of mathematics, a subset of a group G is a subgroup of G if the members of that subset form a group with respect to the group operation in G. Formally, given a group (mathematics), group under a binary operation ...

''H'' with support on a subset ''K'' of ''H'' to class functions on a group ''G'' . It was introduced by as a generalization and simplification of an isometry used by in their

proof Proof most often refers to: * Proof (truth), argument or sufficient evidence for the truth of a proposition * Alcohol proof, a measure of an alcoholic drink's strength Proof may also refer to: Mathematics and formal logic * Formal proof, a co ...

of the

odd order theorem Odd means unpaired, occasional, strange or unusual, or a person who is viewed as eccentric. Odd may also refer to: __NOTOC__ Mathematics * Even and odd numbers, an integer is odd if dividing by two does not yield an integer * Even and odd functio ...

, and was used by in his revision of the

character theory In mathematics, more specifically in group theory, the character of a group representation is a function on the group that associates to each group element the trace of the corresponding matrix. The character carries the essential information a ...

of the odd order theorem.

is a

conjecture In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), ha ...

relating the numbers of characters of blocks of a finite group to the numbers of characters of blocks of local subgroups.

References

Sources * * * * * Citations

External links

Everett C. Dade
* {{DEFAULTSORT:Dade, Everett Clarence 20th-century American mathematicians 21st-century American mathematicians Living people Year of birth missing (living people) Group theorists Princeton University alumni University of Illinois Urbana-Champaign faculty Putnam Fellows Harvard College alumni